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A113508
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Pentagon-free numbers.
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4
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2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 16, 17, 18, 19, 21, 23, 26, 27, 28, 29, 31, 32, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 49, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 81, 82, 83, 86, 87, 89, 91, 93, 94, 97, 98, 99, 101
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OFFSET
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1,1
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COMMENTS
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Pentagonal number analogy of A112886 (the triangle-free positive integers).
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LINKS
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FORMULA
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{a(n)} = {integers k>1: no divisor of k is a pentagonal number n*(3*n-1)/2}>1}. {a(n)} = {integers k>1: no divisor of k is an element of A000326 > 1}.
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EXAMPLE
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10 is not an element, since 10 = 2 * 5 and 5 is the first nontrivial pentagonal number. 24 is not an element, since 12|24 and 12 is a pentagonal number. 44 is not an element, since 22|44 and 22 is a pentagonal number.
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MATHEMATICA
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Select[Range[2, 101], {} == Intersection[{5, 12, 22, 35, 51, 70, 92}, Divisors[#]] &] (* Giovanni Resta, Jun 13 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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